The measure of angle BAC can be calculated using the equation $\sin ^{-1}\left(\frac{3.1}{4.5}\right)=x$. What is the measure of angle BAC? Round to the nearest whole degree.
A. $0^{\circ}$
B. $1^{\circ}$
C. $44^{\circ}$
D. $48^{\circ}$
Answer (2)
Calculate the arcsin of the given ratio: arcsin ( 4.5 3.1 ) .
Convert the result from radians to degrees.
Round the degree value to the nearest whole number.
The measure of angle BAC is approximately: 4 4 ∘ .
Explanation
Problem Analysis We are given that the measure of angle BAC, denoted as x , can be calculated using the equation sin − 1 ( 4.5 3.1 ) = x . Our goal is to find the value of x in degrees, rounded to the nearest whole degree.
Solution Plan First, we need to calculate the value of x in radians using the inverse sine function: x = sin − 1 ( 4.5 3.1 ) .
Then, we convert the value of x from radians to degrees using the formula: degrees = radians × π 180 .
Calculating the angle Calculating the value of x in degrees: x = sin − 1 ( 4.5 3.1 ) ≈ 43.542 2 ∘ .
Rounding the result Rounding the calculated degree value to the nearest whole degree, we get x ≈ 4 4 ∘ .
Final Answer Therefore, the measure of angle BAC is approximately 4 4 ∘ .
Examples
Imagine you're building a ramp and need to determine the angle of elevation. If the rise of the ramp is 3.1 meters and the length of the ramp is 4.5 meters, you can use the arcsin function to find the angle. This ensures the ramp is safe and meets the required specifications. Knowing how to calculate angles using trigonometric functions is crucial in construction, engineering, and many other fields.
The measure of angle BAC can be found by calculating sin − 1 ( 4.5 3.1 ) , which is approximately 43.54 degrees. Rounding this value to the nearest whole degree gives us 4 4 ∘ . Thus, the correct option is C. 4 4 ∘ .
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